Here we intend to address this challenge of verifying
Altshuler and Shklovskii prediction [1]}.
We shall illustrate in detail that a straight forward
study of the number variance using local unfolding is fraught
with ambiguities. Therefore, it is clear that a different tack is needed.
Here we will suggest that a couple of new measures, which are based on
singular value decomposition (SVD) method. This method
has been used to classify whether a system follows
Wigner or Poisson statistics
[2]}, [3]}, [4]},
and recently to identifying non-ergodic extended signature in the
Rosenzweig-Porter model [5]}.
As we shall demonstrate, using the SVD method to replace the short
range unfolding provides a clearer way to study the
the behavior of the energy spectrum beyond the Thouless energy.
